1
WB JEE 2020
MCQ (Single Correct Answer)
+1
-0.25
Change Language
The unit vector in ZOX plane, making angles $$45^\circ $$ and $$60^\circ $$ respectively with $$\alpha = 2\widehat i + 2\widehat j - \widehat k$$ and $$\beta = \widehat j - \widehat k$$ is
A
$${1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat j$$
B
$${1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat k$$
C
$${1 \over {\sqrt 2 }}\widehat i - {1 \over {\sqrt 2 }}\widehat j$$
D
$${1 \over {\sqrt 2 }}\widehat i + {1 \over {\sqrt 2 }}\widehat k$$
2
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$\widehat \alpha $$, $$\widehat \beta $$, $$\widehat \gamma $$ be three unit vectors such that $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )$$ where $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = $$$$(\widehat \alpha \,.\,\widehat \gamma )\widehat \beta - (\widehat \alpha \,.\,\widehat \beta )\widehat \gamma $$. If $$\widehat \beta $$ is not parallel to $$\widehat \gamma $$, then the angle between $$\widehat \alpha $$ and $$\widehat \beta $$ is
A
$${{5\pi } \over 6}$$
B
$${{\pi } \over 6}$$
C
$${{\pi } \over 3}$$
D
$${{2\pi } \over 3}$$
3
WB JEE 2019
MCQ (Single Correct Answer)
+2
-0.5
Change Language
The position vectors of the points A, B, C and D are $$3\widehat i - 2\widehat j - \widehat k$$, $$2\widehat i - 3\widehat j + 2\widehat k$$, $$5\widehat i - \widehat j + 2\widehat k$$ and $$4\widehat i - \widehat j - \lambda \widehat k$$, respectively. If the points A, B, C and D lie on a plane, the value of $$\lambda$$ is
A
0
B
1
C
2
D
$$-$$ 4
4
WB JEE 2018
MCQ (Single Correct Answer)
+2
-0.5
Change Language
Let $$\overrightarrow \alpha $$ = $$\widehat i + \widehat j + \widehat k$$, $$\overrightarrow \beta $$ = $$\widehat i - \widehat j - \widehat k$$ and $${\overrightarrow \gamma }$$ = $$ - \widehat i - \widehat j - \widehat k$$ be three vectors. A vector $$\overrightarrow \delta $$, in the plane of $$\overrightarrow \alpha $$ and $$\overrightarrow \beta $$, whose projection on $${\overrightarrow \gamma }$$ is $${1 \over {\sqrt 3 }}$$, is given by
A
$$ - \widehat i - 3\widehat j - 3\widehat k$$
B
$$\widehat i - 3\widehat j - 3\widehat k$$
C
$$ - \widehat i + 3\widehat j + 3\widehat k$$
D
$$\widehat i + 3\widehat j - 3\widehat k$$
WB JEE Subjects
EXAM MAP
Medical
NEET
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
CBSE
Class 12